Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome

Minimal graphic functions on manifolds of non-negative Ricci curvature

We study minimal graphic functions on complete Riemannian manifolds \Si with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with such growth via splitting for tangent cones of \Si at infinity. When, in contrast, we do not impose any growth restrictions for minimal graphic functions, we also obtain a Liouville type theorem under a certain non-radial Ricci curvature decay condition on \Si. In particular, the borderline for the Ricci curvature decay is sharp by our example in the last section.Comment: 38 page

Chromospheric Evaporation in an X1.0 Flare on 2014 March 29 Observed with IRIS and EIS

Chromospheric evaporation refers to dynamic mass motions in flare loops as a result of rapid energy deposition in the chromosphere. These have been observed as blueshifts in X-ray and extreme-ultraviolet (EUV) spectral lines corresponding to upward motions at a few tens to a few hundreds of km/s. Past spectroscopic observations have also revealed a dominant stationary component, in addition to the blueshifted component, in emission lines formed at high temperatures (~10 MK). This is contradictory to evaporation models predicting predominant blueshifts in hot lines. The recently launched Interface Region Imaging Spectrograph (IRIS) provides high resolution imaging and spectroscopic observations that focus on the chromosphere and transition region in the UV passband. Using the new IRIS observations, combined with coordinated observations from the EUV Imaging Spectrometer, we study the chromospheric evaporation process from the upper chromosphere to corona during an X1.0 flare on 2014 March 29. We find evident evaporation signatures, characterized by Doppler shifts and line broadening, at two flare ribbons separating from each other, suggesting that chromospheric evaporation takes place in successively formed flaring loops throughout the flare. More importantly, we detect dominant blueshifts in the high temperature Fe XXI line (~10 MK), in agreement with theoretical predictions. We also find that, in this flare, gentle evaporation occurs at some locations in the rise phase of the flare, while explosive evaporation is detected at some other locations near the peak of the flare. There is a conversion from gentle to explosive evaporation as the flare evolves.Comment: ApJ in pres

A measure of watershed nonlinearity: interpreting a variable instantaneous unit hydrograph model on two vastly different sized watersheds

The linear unit hydrograph used in hydrologic design analysis and flood forecasting is known as the transfer function and the kernel function in time series analysis and systems theory, respectively. This paper reviews the use of an input-dependent or variable kernel in a linear convolution integral as a quasi-nonlinear approach to unify nonlinear overland flow, channel routing and catchment runoff processes. The conceptual model of a variable instantaneous unit hydrograph (IUH) is characterized by a nonlinear storage-discharge relation, <i>q</i> = <i>c</i><sup>N</sup>s<sup>N</sup>, where the storage exponent <i>N</i> is an index or degree of watershed nonlinearity, and the scale parameter <i>c</i> is a discharge coefficient. When the causative rainfall excess intensity of a unit hydrograph is known, parameters <i>N</i> and <i>c</i> can be determined directly from its shape factor, which is the product of the unit peak ordinate and the time to peak, an application of the statistical method of moments in its simplest form. The 2-parameter variable IUH model is calibrated by the shape factor method and verified by convolution integral using both the direct and inverse Bakhmeteff varied-flow functions on two watersheds of vastly different sizes, each having a family of four or five unit hydrographs as reported by the well-known Minshall (1960) paper and the seldom-quoted Childs (1958) one, both located in the US. For an 11-hectare catchment near Edwardsville in southern Illinois, calibration for four moderate storms shows an average <i>N</i> value of 1.79, which is 7% higher than the theoretical value of 1.67 by Manning friction law, while the heaviest storm, which is three to six times larger than the next two events in terms of the peak discharge and runoff volume, follows the Chezy law of 1.5. At the other end of scale, for the Naugatuck River at Thomaston in Connecticut having a drainage area of 186.2 km<sup>2</sup>, the average calibrated <i>N</i> value of 2.28 varies from 1.92 for a minor flood to 2.68 for a hurricane-induced flood, all of which lie between the theoretical value of 1.67 for turbulent overland flow and that of 3.0 for laminar overland flow. Based on analytical results from the small Edwardsville catchment, the 2-parameter variable IUH model is found to be defined by a quadruplet of parameters <i>N</i>, <i>c</i>, the storm duration or computational time step Δ<i>t</i>, and the rainfall excess intensity <i>i</i>(0), and that it may be reduced to an 1-parameter one by defaulting the degree of nonlinearity <i>N</i> to 1.67 by Manning friction. For short, intense storms, the essence of the Childs – Minshall nonlinear unit hydrograph phenomenon is encapsulated in a peak flow equation having a single (scale) parameter <i>c</i>, and in which the impact of the rainfall excess intensity increases from the linear assumption by a power of 0.4. To illustrate key steps in generating the direct runoff hydrograph by convolution integral, short examples are given

Overall properties of the Gaia DR1 reference frame

We compare quasar positions of the auxiliary quasar solution with ICRF2 sources using different samples and evaluate the influence on the {\it Gaia} DR1 reference frame owing to the Galactic aberration effect over the J2000.0-J20015.0 period. Then we estimate the global rotation between TGAS with {\it Tycho}-2 proper motion systems to investigate the property of the {\it Gaia} DR1 reference frame. Finally, the Galactic kinematics analysis using the K-M giant proper motions is performed to understand the property of {\it Gaia} DR1 reference frame. The positional comparison between the auxiliary quasar solution and ICRF2 shows negligible orientation and validates the declination bias of $\sim$$-0.1$\mas~in {\it Gaia} quasar positions with respect to ICRF2. Galactic aberration effect is thought to cause an offset $\sim$$0.01$\mas~of the $Z$ axis direction of {\it Gaia} DR1 reference frame. The global rotation between TGAS and {\it Tycho}-2 proper motion systems, obtained by different samples, shows a much smaller value than the claimed value $0.24$\masyr. For the Galactic kinematics analysis of the TGAS K-M giants, we find possible non-zero Galactic rotation components beyond the classical Oort constants: the rigid part $\omega_{Y_G} = -0.38 \pm 0.15$\masyr~and the differential part $\omega^\prime_{Y_G} = -0.29 \pm 0.19$\masyr~around the $Y_G$ axis of Galactic coordinates, which indicates possible residual rotation in {\it Gaia} DR1 reference frame or problems in the current Galactic kinematical model.Comment: 6 pages, 1 figure. Accepted for publication in A&

Molecular Dynamics Study of Bamboo-like Carbon Nanotube Nucleation

MD simulations based on an empirical potential energy surface were used to study the nucleation of bamboo-like carbon nanotubes (BCNTs). The simulations reveal that inner walls of the bamboo structure start to nucleate at the junction between the outer nanotube wall and the catalyst particle. In agreement with experimental results, the simulations show that BCNTs nucleate at higher dissolved carbon concentrations (i.e., feedstock pressures) than those where non-bamboolike carbon nanotubes are nucleated

Computational structure‐based drug design: Predicting target flexibility

The role of molecular modeling in drug design has experienced a significant revamp in the last decade. The increase in computational resources and molecular models, along with software developments, is finally introducing a competitive advantage in early phases of drug discovery. Medium and small companies with strong focus on computational chemistry are being created, some of them having introduced important leads in drug design pipelines. An important source for this success is the extraordinary development of faster and more efficient techniques for describing flexibility in three‐dimensional structural molecular modeling. At different levels, from docking techniques to atomistic molecular dynamics, conformational sampling between receptor and drug results in improved predictions, such as screening enrichment, discovery of transient cavities, etc. In this review article we perform an extensive analysis of these modeling techniques, dividing them into high and low throughput, and emphasizing in their application to drug design studies. We finalize the review with a section describing our Monte Carlo method, PELE, recently highlighted as an outstanding advance in an international blind competition and industrial benchmarks.We acknowledge the BSC-CRG-IRB Joint Research Program in Computational Biology. This work was supported by a grant from the Spanish Government CTQ2016-79138-R.J.I. acknowledges support from SVP-2014-068797, awarded by the Spanish Government.Peer ReviewedPostprint (author's final draft